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If the determinant of a 3x3 matrix A is |A| = 9, find the value of |adj((A/3)^(-1))|.
- 1/3
- 1
- 3
- 9
Correct answer: 9
Solution
For a 3x3 matrix M: |adj(M)| = |M|^(n-1) = |M|². Here M = (A/3)^(-1). |A/3| = |A|/3³ = 9/27 = 1/3. |(A/3)^(-1)| = 1/(1/3) = 3. |adj((A/3)^(-1))| = 3² = 9.
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